Generic strange duality for $K3$ surfaces

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Abstract

Strange duality is shown to hold over generic $K3$ surfaces in a large number of cases. The isomorphism for elliptic $K3$ surfaces is established first via Fourier–Mukai techniques. Applications to Brill–Noether theory for sheaves on $K3$ surfaces are also obtained. The appendix, written by Kota Yoshioka, discusses the behavior of the moduli spaces under change of polarization, as needed in the argument.